Abstract
A two-dimensional central limit theorem for the eigenvalues of
Funding source: Research Grants Council, University Grants Committee
Award Identifier / Grant number: 17302514
Award Identifier / Grant number: 17305617
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11501376
Funding source: Natural Science Foundation of Guangdong Province
Award Identifier / Grant number: 2015A030310241
Funding statement: Lau is supported by GRF (Project No. 17302514 and 17305617) of the Research Grants Council of Hong Kong. Wang is supported by the National Natural Science Foundation of China (Grant No. 11501376), Guangdong Province Natural Science Foundation (Grant No. 2015A030310241) and Natural Science Foundation of Shenzhen University (Grant No. 201541).
Acknowledgements
The authors would like to thank Prof. Zeev Rudnick for valuable comments and Dr. Guangyue Han for helpful discussions.
References
[1]
A. Andrianov,
Spherical functions for
[2] P. Billingsley, On the central limit theorem for the prime divisor functions, Amer. Math. Monthly 76 (1969), 132â139. 10.1080/00029890.1969.12000157Suche in Google Scholar
[3] V. Blomer and P. Maga, The sup-norm problem for PGL(4), Int. Math. Res. Not. IMRN 2015 (2015), 5311â5332. 10.1093/imrn/rnu100Suche in Google Scholar
[4] P. Bourgade, C. Hughes, A. Nikeghbali and M. Yor, The characteristic polynomial of a random unitary matrix: A probabilistic approach, Duke Math. J. 145 (2008), 45â69. 10.1215/00127094-2008-046Suche in Google Scholar
[5] A. Bucur, C. David, B. Feigon, M. Lalin and K. Sinha, Distribution of zeta zeroes of ArtinâSchreier covers, Math. Res. Lett. 19 (2012), 1329â1356. 10.4310/MRL.2012.v19.n6.a12Suche in Google Scholar
[6] P. J. Cho and H. H. Kim, Central limit theorem for Artin L-functions, Int. J. Number Theory 13 (2017), 1â14. 10.1142/S1793042117500014Suche in Google Scholar
[7] J. B. Conrey, W. Duke and D. W. Farmer, The distribution of the eigenvalues of Hecke operators, Acta Arith. 78 (1997), 405â409. 10.4064/aa-78-4-405-409Suche in Google Scholar
[8] D. Faifman and Z. Rudnick, Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field, Compos. Math. 146 (2010), 81â101. 10.1112/S0010437X09004308Suche in Google Scholar
[9] K. Fukuyama and Y. Ueno, On the central limit theorem and the law of the iterated logarithm, Statist. Probab. Lett. 78 (2008), 1384â1387. 10.1016/j.spl.2007.12.014Suche in Google Scholar
[10] W. Fulton, Representation Theory. A first Course, Grad. Texts in Math. 129, Springer, New York, 1991. Suche in Google Scholar
[11] R. G. Gallager, Stochastic Processes. Theory for Applications, Cambridge University Press, Cambridge, 2013. 10.1017/CBO9781139626514Suche in Google Scholar
[12]
D. Goldfeld,
Automorphic Forms and L-functions for the Group
[13] L. Hörmander, The Analysis of Linear Partial Differential Operators I, 2nd ed., Springer, Berlin, 1990. Suche in Google Scholar
[14] B. Hough, The distribution of the logarithm in an orthogonal and a symplectic family of L-functions, Forum Math. 26 (2014), 523â546; Erratum, Forum Math. 27 (2015), 3783â3784. 10.1515/forum-2011-0105Suche in Google Scholar
[15] P. Kurlberg and Z. Rudnick, The fluctuations in the number of points on a hyperelliptic curve over a finite field, J. Number Theory 129 (2009), 580â587. 10.1016/j.jnt.2008.09.004Suche in Google Scholar
[16]
Y.-K. Lau and Y. Wang,
Absolute values of L-functions for
[17] I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Oxford University Press, Oxford, 1995. 10.1093/oso/9780198534891.001.0001Suche in Google Scholar
[18]
J. Matz and N. Templier,
SatoâTate equidistribution for families of HeckeâMaass forms on
[19] H. Nagoshi, Distribution of Hecke eigenvalues, Proc. Amer. Math. Soc. 134 (2006), 3097â3106. 10.1090/S0002-9939-06-08709-0Suche in Google Scholar
[20] V. V. Petrov, A theorem on the law of the iterated logarithm, Theory Probab. Appl. 16 (1971), 700â702. 10.1137/1116078Suche in Google Scholar
[21] N. Prabhu and K. Sinha, Fluctuations in the distribution of Hecke eigenvalues about the SatoâTate measure, Int. Math. Res. Not. IMRN 2017 (2017), 10.1093/imrn/rnx238. 10.1093/imrn/rnx238Suche in Google Scholar
[22]
J. P. Serre,
RĂ©partition asymptotique des valeurs propres de lâopĂ©rateur de Hecke
[23] G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, Cambridge, 1995. Suche in Google Scholar
[24] A. W. van der Vaart, Asymptotic Statistics, Cambridge University Press, Cambridge, 1998. 10.1017/CBO9780511802256Suche in Google Scholar
[25] Y. Wang, The quantitative distribution of Hecke eigenvalues, Bull. Aust. Math. Soc. 90 (2014), 28â36. 10.1017/S0004972714000070Suche in Google Scholar
[26] M. Xiong, Statistics of the zeros of zeta functions in a family of curves over a finite field, Int. Math. Res. Not. IMRN 2010 (2010), 3489â3518. 10.1093/imrn/rnq015Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Sharp maximal estimates for multilinear commutators of multilinear strongly singular CalderĂłnâZygmund operators and applications
- Infinite-dimensional triangularizable algebras
- Expansion for the product of matrices in groups
- Asphericity of positive free product length 4 relative group presentations
- Unitary representations with non-zero Dirac cohomology for complex E6
- On middle cohomology of special ArtinâSchreier varieties and finite Heisenberg groups
- Normal elements of noncommutative Iwasawa algebras over SL3(â€_p)
- Regularity properties of Schrödinger equations in vector-valued spaces and applications
- Statistics of Hecke eigenvalues for GL(đ)
- Bilinear CalderĂłnâZygmund operators on products of variable Hardy spaces
- On the Reidemeister spectrum of an Abelian group
- Dense free subgroups of automorphism groups of homogeneous partially ordered sets
- Left semi-braces and solutions of the YangâBaxter equation
- On the automorphism group of a symplectic half-flat 6-manifold
Artikel in diesem Heft
- Frontmatter
- Sharp maximal estimates for multilinear commutators of multilinear strongly singular CalderĂłnâZygmund operators and applications
- Infinite-dimensional triangularizable algebras
- Expansion for the product of matrices in groups
- Asphericity of positive free product length 4 relative group presentations
- Unitary representations with non-zero Dirac cohomology for complex E6
- On middle cohomology of special ArtinâSchreier varieties and finite Heisenberg groups
- Normal elements of noncommutative Iwasawa algebras over SL3(â€_p)
- Regularity properties of Schrödinger equations in vector-valued spaces and applications
- Statistics of Hecke eigenvalues for GL(đ)
- Bilinear CalderĂłnâZygmund operators on products of variable Hardy spaces
- On the Reidemeister spectrum of an Abelian group
- Dense free subgroups of automorphism groups of homogeneous partially ordered sets
- Left semi-braces and solutions of the YangâBaxter equation
- On the automorphism group of a symplectic half-flat 6-manifold